Question

Alpha particles (charge = +2e, mass = 6.68 × 10-27 kg) are accelerated in a cyclotron to a final orbit radius of 0.35 m. The particles undergo uniform circular motion in a magnetic field equal to 0.9 T. What is the cyclotron frequency of the alpha particles?

Answer 1

Given that B = 0.9 T mass of alpha particle = 6.68 * 10^-27 kg charge of alpha particle = +2e ; Radius r = 0.35m q = +2e ==> +2(1.6 * 10^-19 C)

We know that  F = m² / r ----------------- (1) F = qVB -------------------- (2) From equation 1 & 2 m² / r = qVB ==> m / r = qB / r = qB/m ===> r/ = m/qB   Velocity = distance / time = 2r / T Time period T = 2r / V = 2(r / V) Therefore cyclotron frequency = V = 2 * m / qB = 2*(6.68*10^-27) / 2 * (1.6*10^-19)*(0.9T) = 4.195 * 10^-26 / 2.88 * 10^-19 = 1.4565 * 10^-7 sec   V = 0.14 s